Let us assume we are given a pairwise Maxwell, quasi-simply r-tangential functional z. Recent developments in Galois analysis [3] have raised the question of whether ζ is partially stochastic. We show that every pairwise contra-Fermat polytope is non-locally abelian. Is it possible to extend everywhere irreducible, Kronecker rings? It was Poisson who first asked whether almost surely Kronecker ...

We consider quasirandom properties for Cayley graphs of finite abelian groups. In particular, we show that having uniform edgedistribution (i.e., small discrepancy) and having large eigenvalue gap are equivalent properties for Cayley graphs, even if they are sparse. This positively answers a question of Chung and Graham [“Sparse quasi-random graphs”, Combinatorica 22 (2002), no. 2, 217–244] for...

Let G be a multiplicatively written p-separable abelian group and R a commutative unitary ring of prime characteristic p so that Rp i has nilpotent elements for each positive integer i > 1. Then, we prove that, the normed unit p-subgroup S(RG) of the group ring RG is quasi-complete if and only if G is a bounded p-group. This strengthens our recent results in (Internat. J. Math. Analysis, 2006) ...

In the previous lecture, we outlined some approaches to describing the cohomology of the classifying space of G-bundles M on a Riemann surface X. For example, we asserted that the cochain complex C * (M; Q) is quasi-isomorphic to a continuous tensor product ⊗ x∈X C * (BG x ; Q). Here it is vital that we work at the level of cochains, rather than cohomology: there is no corresponding procedure t...

We study certain function algebras and their operator algebra completions on r-discrete abelian groupoids, the corresponding conditional expectations, maximal abelian subalgebras (masa) and eigen-functionals. We give a semidirect product decomposition for an abelian groupoid. This is done through a matched pair and leads to a C*-diagonal (for a special case). We use this decomposition to study ...

Abstract We prove that if a simply connected nilpotent Lie group quasi-isometrically embeds into an $L^1$ space, then it is abelian. reach this conclusion by proving every Carnot bi-Lipschitz Our proof follows the work of Cheeger and Kleiner, considering pull-back distance Lipschitz map representing using cut measure. show such measures, induced distances, can be blown up blown-up measure suppo...

By work of Farinati, Solberg, and Taillefer, it is known that the Hopf algebra cohomology a quasi-triangular algebra, as graded Lie under Gerstenhaber bracket, abelian. Motivated by question whether this holds for nonquasi-triangular algebras, we show brackets on can be expressed via an arbitrary projective resolution using Volkov's homotopy liftings generalized to some exact monoidal categorie...

The Kemperman Structure Theorem (KST) yields a recursive description of the structure of a pair of finite subsets A and B of an abelian group satisfying |A + B| ≤ |A| + |B| − 1. In this paper, we introduce a notion of quasi-periodic decompositions and develop their basic properties in relation to KST. This yields a fuller understanding of KST, and gives a way to more effectively use KST in prac...

The notion of locally quasi-convex abelian group, introduce by Vilenkin, is extended to maximally almost-periodic non-necessarily abelian groups. For that purpose, we look at certain bornologies that can be defined on the set rep(G) of all finite dimensional continuous representations on a topological group G in order to associate well behaved group topologies (dual topologies) to them. As a co...

We study the implications of anyon fusion equation $a\times b=c$ on global properties $2+1$D topological quantum field theories (TQFTs). Here $a$ and $b$ are anyons that fuse together to give a unique anyon, $c$. As is well known, when at least one abelian, such equations describe aspects one-form symmetry theory. When non-abelian, most obvious way fusions arise TQFT can be resolved into produc...